Plate 1. Portrait of Simon Stevin by an unknown artist. Library of Leyden University.
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1 The renovation of the arts and sciences by the Renaissance has been especially glorious in Italy and the Netherlands. Among the outstanding scholars of that period Simon Stevin, born at Bruges and living at Lelden, is one of the most interesting. Although little is known about his life, his marked personality speaks clear I y to us through his writings. He wrote on Mathematics, Mechanics, Hydrostatics, Astronomy, Navigation and technical and military matters; he introduced decimal fractions and measures; he prepared the theorem of the parallelogram of forces; he established fundamental laws in hydrostatics; he was one of the early defenders of the Copernican system and he explained loxodromic sailing, improved the windmills, proposed equal temperament in music and improved the construction of fortifications. He always combined purely theoretical investigations with their practical applications. A survey of his work conveys at the same time a vivid picture of the exact sciences about The author, the late E. J. Dijksterhuis ( ), was a professor of history of science at the universities of Utrecht and Leyden. He wrote books on Euclid and on ArchImedes' mathematics and mechanics, and he became widely known outside the circle of historians of SCience by his extensive study on "The Mechanization of the World Picture" (1950; engl. transl. 1961). Of his standard work on Simon Stevin (written In the Dutch language), the present book Is a shortened version In English, adapted to the educated, non-specialist reader.
2 SIMON STEVIN
3 Plate 1. Portrait of Simon Stevin by an unknown artist. Library of Leyden University.
4 SIMON STEVIN Science in the Netherlands around 1600 BY E. J. DIJKSTERHUIS MARTINUS NIJHOFF / THE HAGUE 1970
5 ISBN-13: e-isbn-13: DOl: / by Martinus NijhojJ, The Hague, Netherlands All rights reserved, including the right to translate or to reproduce this book or parts thereof in any form
6 CONTENTS EDITORS' PREFACE INTRODUCTION 1 1. STEVINS' LIFE 4 II. MATHEMATICS 14 Introduction 14 Sixteenth-Century Mathematics 14 Stevin's Mathematical Work De Thiende Tables of Interest Arithmetic and Algebra Introduction Geometrical Numbers Algebraic Numbers Equations The Quadratic Equation The Cubic Equation Negative Roots The Equation of the Fourth Degree The Rule "Algebra" New Methods The Translation of Diophantus's Algebra The Practice of Arithmetic The Doctrine of Ratios Theory of Irrational Quantities Geometry Introduction Geometrical Problems Geometrical Instruments Trigonometry Construction of an Ellipse Didactics 43 IX
7 VI CONTENTS 4.7 Semi-regular Polyhedra Augmented Polyhedra Perspective 46 III. MECHANICS Introduction Aristotelean and Archimedean Mechanics Stevin's Criticism of the Principle of Virtual Displacements The Art of Weighing (De Weeghconst) Definitions and Postulates. The Theory of the Lever The Wreath of Spheres (Clootcrans) Oblique Forces Three Forces in Equilibrium Centres of Gravity The Practice of Weighing (Weeghdaet) Resistances An Experiment on Falling Bodies Instruments and Machines The Pressure of the Bridle (Toomprang) 61 IV. HYDROSTATICS Introduction The Archimedean Principle The Force Exerted on the Bottom 66 4, The Force Exerted on the Walls The Problem of the Diver On Floating Top-heaviness (Vlietende Topswaerheyt) Summary 69 V. AsTRONOMY Introduction The Heavenly Motions (Hemelloop) Stevin's Method The Plan of the Work Copernican Astronomy Theological Opposition The Nova Zembla Phenomenon The Tides 80 VI. NAVIGATION Introduction The Sailings (Zeylstreken) Great-circle Sailing Loxodromic Sailing The Haven-finding Art (Havenvinding) Introduction 87
8 CONTENTS VII 5.2 The Memoir of Plancius Stevin's Method of Haven-finding 88 VII. TECHNOLOGY Introduction Mills Introduction The Mechanism of a Water-miII Theory of the MiII Stevin on MiIIs (Van de Molens) Sluices and Locks Various Kinds of Sluices The Swivel-gate Lock Hydraulic Engineering Geomorphology The Sailing Chariot 104 VIII. MILITARY SCIENCE 106 A. Fortification 106 B. The Marking out of Army Camps (Castrametatio) 110 IX. ARCHITECTURE Introduction Town-Planning House-Building 115 X. DOUBLE-ENTRY BOOK-KEEPING Introduction Mercantile Book-keeping Princely Book-keeping 118 XI. MUSIC 120 XII. CIVIC MATTERS 123 A. The Citizen 123 B. The Prince 124 XIII. STEVIN AND THE DUTCH LANGUAGE 126 XIV. STEVIN'S PERSONALITY 130 XV. STEVIN'S WORKS 134
9 PREFACE The works of Simon Stevin are most interesting for the history of science, because they have such a wide scope and reflect so clearly the development of scientific knowledge around 1600 in central Europe. The recent publication of his Principal Works, with an English translation, has again attracted attention to his fascinating personality. The book on Stevin by Professor E. J. Dijksterhuis, originally published in the Dutch language, is an excellent introduction to the life and works of this remarkable Netherlander. Dijksterhuis prepared a somewhat condensed English edition, adapted to the foreign reader. Because of his untimely death, publication had to be deferred until the undersigned were able to undertake the editorial work. The Royal Netherlands Academy of Sciences, Amsterdam, allowed a grant, through which a linguistic revision of the text was made possible. We are very grateful to Miss C. Dikshoorn for the care with which she carried out this task and prepared the text for the press. A few supplementary notes have been added, for which we are personally responsible and which have been marked with our initials (R.H. or M.M.). Messrs Martinus Nijhoff, The Hague, who published the original Dutch edition, have kindly agreed to bring out also the English version and have given all their attention to this publication. R. HOOYKAAS M. G. J. MINNAERT
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